Question

A company is considering proposal of purchasing a machine either by making
full payment of ₹ 4,000 or by leasing it for four years at an annual rate of ₹ 1,250. Which course
of action is preferable if the company can borrow money at 14% compounded annually ?​

Answer 1

$\large\underline{\sf{Solution-}}$

Here, to find whether lèasing for 4 years at Rs 1250 at the rate of 14 % per annum compounded annually is preferable or full payment of Rs 4000 is better, we have to find the present value of Rs 1250 for 4 years at the rate of 14 % per annum compounded annually.

• If the Present value < Purchase Value, then lèasing is preferable.

and

• If Present value > Purchase Value, then purchasing is preferable.

So,

Here, we have

Purchase Price = Rs 4000

• Amount paid every year, R = Rs 1250

• Rate of interest, i = 0.14 per rupee

• Time, n = 4 years

• Let the present value be Rs P.

Then,

Present value is given by

$\rm :\longmapsto\:P \: = \: \dfrac{R\bigg( 1 - {(1 + i)}^{ - n} \bigg) }{i}$

On substituting the values of R, i and n, we get

$\rm :\longmapsto\:P \: = \: \dfrac{1250\bigg( 1 - {(1 + 0.14)}^{ - 4} \bigg) }{0.14}$

$\rm :\longmapsto\:P \: = \: \dfrac{1250\bigg( 1 - {(1.14)}^{ - 4} \bigg) }{0.14}$

$\sf \: Let \: x = {(1.14)}^{ - 4} \: \: \: \: \: \\ \sf \: logx \: = - 4 log(1.14) \\ \sf \: logx = - 4 \times 0.0569 \\ \sf \: logx = - 0.2276 \: \: \: \: \: \: \\ \sf \: logx = \overline{1}.7724 \: \: \: \: \: \: \: \: \: \\ \sf \: x = antilog(\overline{1}.7724) \\ \sf \: x = 0.5922 \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\rm :\longmapsto\:P \: = \: \dfrac{1250\bigg( 1 - 0.5922 \bigg) }{0.14}$

$\rm :\longmapsto\:P \: = \: \dfrac{1250\bigg(0.4078 \bigg) }{0.14}$

$\rm :\longmapsto\:P = 1250 \times 2.913$

$\rm :\implies\: \: P \: = \: Rs \: 3641.25$

$\rm :\implies\:Present \: value \: < \:Purchase \:price$

$\rm :\implies\:Leasing \: is \: preferable.$